This gives me the following error:
Bad expression value 'Expression 1' detected in parameter 'Thermal Conductivity' in object '/LIBRARY/MATERIAL:Zirconium/PROPERTIES/THERMAL CONDUCTIVITY'.
CEL error:
The following unrecognised name was referenced: K.

Which basically says that I can't use K as the input to my function?

Hi ajhunte !

from the info you have given, it seems that you have tried to modify an element's properties from the MATERIALs library. Something is wrong with you re-definition. Could you provide additional info - what module of ANSYS do you use?

Possible solutions for the definition of temperature dependence of thermal conductivity:
1. if you use Transient module, you can specify temperature dependence of thermal conductivity in a Table form in the section 'Engineering Data'.
2. if you use FLUENT module, you can define a User-Defined Function (code it in C) and either compile or interpret it, and then use this function in material's properties specification. (There is a reference guide on how to make the User-Defined Functions in FLUENT).